Finite Group Databasebeta

← #28476815

Subgroups — #28476815

Order 15104.

440 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426665C211yesmaximal, characteristic
2#21424238C212yesmaximal
3#21421922C211yesmaximal, characteristic
4#21421921C212yesmaximal
5C59×#1272C211yesmaximal, characteristic
6C2×#14273725C411yescharacteristic
7C2×Q8×Dic59C411yescharacteristic
8C2×#14273692C411yescharacteristic
9#16837308C2211yescharacteristic
10#16837299—22no—
11#16837271C411yescharacteristic
12#16837253—22no—
13C42×Dic59C2211yescharacteristic
14#16837157C2212yes—
15#16837156—22no—
16#16837156—22no—
17C59×#391C2211yescharacteristic
18C59×#336C2212yes—
19C22×Dic118C2×C411yescharacteristic
20C22×C59⋊C8—22no—
21#14273725—22no—
22#14273725C814yescomplemented
23Q8×Dic59—42no—
24#14273692—42no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59C2×C411yescharacteristic
27C2×Dic59⋊C4—22no—
28C2×Dic59⋊C4—22no—
29C2×Dic59⋊C4—21no—
30C2×C4×Dic59—21no—
31C2×C4×Dic59—21no—
32C2×C4×Dic59C2×C411yescharacteristic
33C2×C4×Dic59C2×C411yescharacteristic
34C2×C4×Dic59D412yes—
35C2×C4×Dic59D412yes—
36C59⋊#95—22no—
37C22×Q8×C59C2×C411yescharacteristic
38C22×C8×C59—22no—
39C2×C4⋊C4×C59C2×C411yescharacteristic
40C2×C42×C59C2311yescharacteristic
41#95×C59—22no—
42C2×Q8×C59—21no—
43C2×Q8×C59—41no—
44C2×Q8×C59—41no—
45C2×Q8×C59C2×C812yes—
46C22×C4×C59—21no—
47C22×C4×C59—21no—
48C22×C4×C59C22×C411yescharacteristic
49C22×C4×C59C2×D412yes—
50C22×Dic59—21no—
51C22×Dic59—21no—
52C22×Dic59C22⋊C411yescharacteristic
53C22×Dic59C22⋊C412yes—
54C22×Dic59C22⋊C411yescharacteristic
55C2×Dic118—21no—
56C2×Dic118—41no—
57C2×Dic118—41no—
58C2×Dic118C2×C812yes—
59C2×C8×C59—42no—
60C2×C8×C59—42no—
61C2×C8×C59—42no—
62C4⋊C4×C59—41no—
63C42×C59—41no—
64C4⋊Dic59—42no—
65C4⋊Dic59—41no—
66Dic59⋊C4—28no—
67Dic59⋊C4—44no—
68Dic59⋊C4—42no—
69C4×Dic59—22no—
70C4×Dic59—22no—
71C4×Dic59—22no—
72C4×Dic59—42no—
73C4×Dic59—42no—
74C4×Dic59—42no—
75C4×Dic59C2×C812yes—
76C4×Dic59M1612yes—
77C2×C59⋊C8—42no—
78C2×C59⋊C8—42no—
79C2×C59⋊C8—42no—
80C23×C59C2×C22⋊C411yescharacteristic
81Q8×C59—42no—
82Q8×C59—42no—
83C2×C4×C59—22no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—41no—
89C2×C4×C59—41no—
90C2×C4×C59—41no—
91C2×C4×C59—42no—
92C2×C4×C59C22×C811yescharacteristic
93C2×C4×C59C2×M1611yescharacteristic
94C2×C4×C59#13712yes—
95C2×C4×C59#13712yes—
96C2×Dic59—22no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—22no—
100C2×Dic59—21no—
101C2×Dic59—22no—
102C2×Dic59—41no—
103C2×Dic59—41no—
104C2×Dic59—41no—
105C2×Dic59—42no—
106C2×Dic59C22⋊C814yes—
107C2×Dic59#10012yes—
108Dic118—42no—
109Dic118—42no—
110C8×C59—82no—
111C59⋊C8—82no—
112#7605—591nomaximal, Sylow
113C22×C59C2×C22⋊C811yescharacteristic
114C22×C59#41011yescharacteristic
115C22×C59C2×#10011yescharacteristic
116C22×C59#41912yes—
117C22×C59#42112yes—
118C4×C59—21no—
119C4×C59—21no—
120C4×C59—22no—
121C4×C59—22no—
122C4×C59—42no—
123C4×C59—81no—
124Dic59—22no—
125Dic59—24no—
126Dic59—41no—
127Dic59—42no—
128Dic59—81no—
129C4×C4⋊Q8—591no—
130#1839—592no—
131#1272—591no—
132#1272—592no—
133#1272D5911yescharacteristic
134C2×C59#146011yescharacteristic
135C2×C59#147912yes—
136C2×C59#151512yes—
137C2×C59#153611yescharacteristic
138C2×C59#155811yescharacteristic
139C2×C4⋊Q8—591no—
140C2×C4×Q8—591no—
141C2×C4×Q8—591no—
142#391—591no—
143#391C2×D5911yescharacteristic
144#389—1182no—
145#384—591no—
146C4×C4⋊C4—1182no—
147C43—591no—
148#336—592no—
149#336—1182no—
150#336—1182no—
151#336C2×D5912yes—
152C59#760511yescharacteristic, complemented, Sylow
153C22×Q8—591no—
154C22×Q8C4×D5911yescharacteristic
155C22×C8—22no—
156C22×C8—1182no—
157C4⋊Q8—594no—
158C4⋊Q8—1182no—
159C4×Q8—2362no—
160C4×Q8—2362no—
161C2×C4⋊C4—591no—
162C2×C4⋊C4—1182no—
163C2×C4⋊C4—1181no—
164C2×C4⋊C4—1181no—
165C2×C4⋊C4—1182no—
166C2×C4⋊C4C4×D5911yescharacteristic
167C2×C42—591no—
168C2×C42—591no—
169C2×C42—592no—
170C2×C42—592no—
171C2×C42—1181no—
172C2×C42—1181no—
173C2×C42C22×D5911yescharacteristic
174#95—22no—
175#95—1182no—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—592no—
180C2×Q8—1181no—
181C2×Q8—2361no—
182C2×Q8—2361no—
183C2×Q8C8×D5912yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—591no—
187C22×C4—592no—
188C22×C4—591no—
189C22×C4—1181no—
190C22×C4—1181no—
191C22×C4C2×C4×D5911yescharacteristic
192C22×C4D4×D5912yes—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—2362no—
197C2×C8—2362no—
198C2×C8—2362no—
199C4⋊C4—41no—
200C4⋊C4—1188no—
201C4⋊C4—2361no—
202C4⋊C4—2362no—
203C4⋊C4—2362no—
204C4⋊C4—2364no—
205C42—41no—
206C42—592no—
207C42—592no—
208C42—1182no—
209C42—1182no—
210C42—1182no—
211C42—2362no—
212C42—2362no—
213C42—2362no—
214C23C22⋊C4×D5911yescharacteristic
215Q8—42no—
216Q8—42no—
217Q8—2362no—
218Q8—2362no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—592no—
229C2×C4—594no—
230C2×C4—1182no—
231C2×C4—1182no—
232C2×C4—1182no—
233C2×C4—1181no—
234C2×C4—1182no—
235C2×C4—1182no—
236C2×C4—2361no—
237C2×C4—2362no—
238C2×C4—2361no—
239C2×C4—2361no—
240C2×C4C2×C8×D5911yescharacteristic
241C2×C4M16×D5911yescharacteristic
242C2×C4#1427375612yes—
243C2×C4#1427375912yes—
244C8—82no—
245C8—4722no—
246C22C22⋊C8×D5911yescharacteristic
247C22#1683737411yescharacteristic
248C22#100×D5911yescharacteristic
249C22#1683740912yes—
250C22#1683741712yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—42no—
256C4—81no—
257C4—1184no—
258C4—1182no—
259C4—4721no—
260C4—2362no—
261C4—2361no—
262C2#2142241511yescharacteristic
263C2#2142248912yes—
264C2#2142264512yes—
265C2#2142272911yescharacteristic
266C2#2142282011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC2×C4×C59C22×C8
FrattiniC2×C42C22×D59
FittingC59×#1272C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1272D59
hypocenterC59#7605
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
22. #14273725C8semidirect
152. C59#7605semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214266652
#214242382
#214219222
#214219212
C59×#12722
#760559